00:01
For questions 1, 2, and 3, you have to identify a, b, and c in each of the quadratic equations.
00:06
So let's first take a look at a generic quadratic equation, where we have a, x squared, plus b, x, plus c is equal to 0.
00:18
These are the values that we're asked to find.
00:21
So for question 1, where 5x squared minus 16ax plus 3a squared equals 0, all we have to do is take a look.
00:30
At the values before our x squared and our x and we'll get a and b.
00:36
So here we have 5 and 16a.
00:39
So a is equal to 5.
00:43
B is equal to minus 16a because remember this minus sign it goes with that 16.
00:50
But what about c? c has this funny a squared next to it so that could be confusing.
00:56
But remember all c is is just a number without our x.
01:02
So in this case, c is going to be 3a squared.
01:08
It's going to be all of that.
01:10
Because remember, the variable that we're concerned with in this case is x.
01:14
So let's apply that logic to question two, 12 n squared minus m nx plus m squared x squared.
01:24
So here we have to consider our n.
01:28
So we're going to pretend our n is going to be the x squared in our generic equation.
01:37
So if we replace this x squared with n squared, and the x here with n, that should be a zero at the end, this might make a little bit more sense.
01:50
So here, a is just going to be 12.
01:55
B is going to be minus mx, because remember, we're looking at n now, c is just going to be m squared, x squared.
02:06
So here for equation three, we have k squared, x squared minus 8x h x x minus 7 h squared.
02:14
So this looks a little bit different from our generic equation that we're used to working with.
02:18
So let's rewrite it and let's make sure that we can get it into the proper form.
02:23
So what we're going to do is we're going to move this h squared over, but we're also going to rewrite our middle term here.
02:31
Because if you notice we have our two xes.
02:33
So this really should be 8h times 2x.
02:37
So let's rewrite this.
02:39
So we're going to have 7h squared, and then we're going to have minus 8h2x plus k squared, x squared.
02:52
So let's rewrite our middle term one more time, where we have 7h squared minus 16 hx plus k squared, x squared.
03:03
So here, our generic equation, we have 8x squared plus ex plus c, equals 0.
03:11
In this case, our x squared is just going to be replaced with h squared.
03:16
So our a is going to be 7.
03:19
Our b is going to be minus 16x, and our c is just going to be 1 k squared x squared.
03:28
Now the one i put in because it's not written here, but i wanted to have a numeral there.
03:34
For the remaining questions, we have to find the solution set.
03:37
So we're going to be using factoring in the quadratic equation to solve some of these.
03:41
But it's not in the generic form that we're used to.
03:44
So the generic form that we're used to is a x squared plus bx plus c, and that equals 0.
03:51
So let's get this equation, equation four, into that form.
03:55
So how are we going to do that? well, in equation four, we're going to let x squared equal, let's say z.
04:05
So now our x to the fourth is going to become z minus 17 z plus 16.
04:13
So here, we can use our factoring.
04:17
We can say z here and here.
04:20
And then we need two numbers that when added together equals 17 and when multiplied together equals 16.
04:26
Well, that's going to be 16 and 1.
04:30
And they're both going to be negative.
04:33
That's how we're going to get our negative 17.
04:35
So now we have z minus 1 equals 0.
04:39
And z minus 16 equals zero.
04:43
But remember, z is x squared.
04:46
So let's rewrite that.
04:47
Let's put our x squared back in.
04:49
X squared minus one equals zero, and x squared minus 16 equals zero.
04:56
X squared equals one, and then x squared equals 16.
05:01
X is going to equal the square root of one and it's going to equal the square root of 16.
05:07
I'm running out of room.
05:08
So we'll just put them up here.
05:11
X is equal to 1 and x is equal to 4.
05:16
So we're going to follow that same sort of logic for the remaining questions.
05:21
In 5, let's put this in our generic form where we'll have x to the 4 minus 13 x squared plus 36.
05:32
We're going to let x, well, let's get rid of that x.
05:37
Let's choose a different one.
05:38
Let's let y equal x squared.
05:42
So now we have y squared minus 13 y plus 36.
05:48
So again, we can factor.
05:51
We'll put our y in, and then we're going to use 9 and 4, because when you add those together, they equal 13.
05:57
When you multiply, they get 36.
06:00
And we're going to have negative signs in both places.
06:03
So that's y minus 4.
06:05
Oh, and i forgot to say this is all equal to 0, since we got rid of it on the one side.
06:11
So y minus 4 equals 0, and then y minus 9 is going to equal 0.
06:17
This means y is equal to 4 and y is equal to 9.
06:22
Let's put our x squared back in.
06:24
X squared is equal to 4, x squared is equal to 9, x is equal to the square root of 4, and the square root of 9, 4, 2, and 3.
06:39
Let's look at question 6 here.
06:43
We have a weird formula, but again, we're just going to let, let's pick q.
06:49
Here, it's just going to be x squared minus 4x.
06:54
So now we have q squared plus 7q plus 12.
06:59
Here, we can use our factoring method...